Sunday, January 21, 2018 - Saturday, January 27, 2018

Conversations among Colleagues

Title: Academic Integrity

Date: 01/22/2018

Time: 4:10 PM - 5:00 PM

Place: C109 Wells Hall

Speaker: Dr. Robert Caldwell

Dr. Robert Caldwell, MSU's Ombudsperson, will attend this meeting. This will be an opportunity to ask him questions regarding challenging scenarios many of us have encountered during exam proctoring, grading of tests and projects.

Mathematics Education Colloquium Series

Title: Investigating Subtleties of the Multiplication Principle

Date: 01/23/2018

Time: 1:15 PM - 2:45 PM

Place: 252 EH

Speaker: Elise Lockwood, Oregon State University

Central to introductory probability, and a primary feature of most discrete mathematics courses, the Multiplication Principle is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the ways it is presented in textbooks are surprisingly varied. In this talk, I identify key elements of the principle and present a categorization of statement types that emerged from a textbook analysis. I also incorporate excerpts from a reinvention study that sheds light on how students reason through key elements of the principle. Findings from both the textbook analysis and the reinvention study reveal surprisingly subtle aspects of the multiplication principle that can be made concrete for students through carefully chosen examples. I conclude with a number of potential mathematical and pedagogical implications of the categorization.

Combinatorics and Graph Theory

Title: An Introduction to Stanley's Theory of P-Partitions. I

Date: 01/23/2018

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Bruce Sagan, MSU

Richard Stanley developed a powerful generalization of the theory of integer partitions where the parts of the partition are arranged on any labeled poset P. In this first lecture we will develop some intuition by computing the generating functions for various families of ordinary integer partitions. This will motivate Stanley's generalization which will be discussed in the second lecture. No background will be assumed.

Student Geometry/Topology II

Title: Dualities in Persistent (co)Homology-Part II

Date: 01/24/2018

Time: 4:10 PM - 5:00 PM

Place: C517 Wells Hall

Speaker: Hitesh Gakhar, MSU

For a filtered topological space, its persistent homology is a multi-set of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.

Mathematical Physics and Gauge Theory

We consider the Cauchy problem for the energy-critical defocusing
nonlinear wave equation in four space dimensions. It is known that for
initial data at energy regularity, the solutions exist globally in time
and scatter to free waves. However, the problem is ill-posed for initial
data at super-critical regularity, i.e. for regularities below the
energy regularity.
In this talk we study the super-critical data regime for this Cauchy
problem from a probabilistic point of view, using a randomization
procedure that is based on a unit-scale decomposition of frequency
space. We will present an almost sure global existence and scattering
result for randomized radially symmetric initial data of super-critical
regularity. This is the first almost sure scattering result for an
energy-critical dispersive or hyperbolic equation for scaling
super-critical initial data.
The main novelties of our proof are the introduction of an approximate
Morawetz estimate to the random data setting and new large deviation
estimates for the free wave evolution of randomized radially symmetric data.
This is joint work with Ben Dodson and Dana Mendelson.

Geometry and Topology

Title: The Extended Bogomolny Equations and Teichmuller space

Date: 01/25/2018

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

Speaker: Siqi He, Caltech

We will discuss Witten’s gauge theory approach to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3-dimensional, we call them the extended Bogomolny equations. We will discuss a Donaldson-Ulenbeck-Yau type correspondence of the moduli space of the singular solutions to the Extended Bogomolny equations and Teichmuller space. If time permits, we will also discuss the relationship of the singular solutions moduli space with higher Teichmuller theory. This is joint work with Rafe Mazzeo.

Probability

Title: An invitation to large scale sojourn properties of Brownian motion

Date: 01/25/2018

Time: 3:00 PM - 3:50 PM

Place: C405 Wells Hall

Speaker: Xiaochuan Yang, MSU

For a one dimensional Brownian motion, we consider the sets of times where Brownian motion stays inside some moving boundaries. The boundaries considered are power functions with the power in [0, 1/2]. Since the usual scaling for Brownian motion at time t is square root of t, the sojourn sets we considered describe the recurrence of a Brownian motion around zero. We give large scale geometric properties of these sets using macroscopic dimensions introduced by Barlow and Taylor in the late 80's. The audience of 881/882 might find this talk interesting.